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SUMMARY:Multi-Index Stochastic Collocation (MISC) for Elliptic PDEs with r
 andom data - Lorenzo Tamellini (Università degli Studi di Pavia)
DTSTART:20180206T113000Z
DTEND:20180206T123000Z
UID:TALK99937@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Joakim Beck		(KAUST)\, Abdul-Lateef Haji-Ali
 		(Oxford University)\, Fabio Nobile		(EPFL)\, Raul Tempone		(KAUST)      
   <br></span><br>In this talk we describe the Multi-Index Stochastic Collo
 cation method (MISC) for computing statistics of the solution of an ellipt
 ic PDE with random data. MISC is a combination technique based on mixed di
 fferences of spatial approximations and quadratures over the space of rand
 om data. We propose an optimization procedure to select the most effective
  mixed differences to include in the MISC estimator: such optimization is 
 a crucial step and allows us to build a method that\, provided with suffic
 ient solution regularity\, is potentially more effective than other multi-
 level collocation methods already available in literature. We provide a co
 mplexity analysis both in the case of a finite and an infinite number of r
 andom variables\, showing that in the optimal case the convergence rate of
  MISC is only dictated by the convergence of the deterministic solver appl
 ied to a one dimensional problem. We show the effectiveness of MISC with s
 ome computational tests\, and in particular we discuss how MISC can be eff
 iciently combined with an isogeometric solver for PDE.
LOCATION:Seminar Room 1\, Newton Institute
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